# What are these equations called in English?

I just wonder what these simple equations are called in English? Do they have professional names/terminologies in math?

equation 1: x = a + b - c

equation 2: x = a * b / c

The key is the sign, equation 1 only contains plus and/or minus signs. Equation 2 contains only Multiplication and division signs. a, b, and c are variables, they could be a complex term, or a single known or unknown value.

So, what do I call these two types of equations in English? I know the first one might be called a linear equation, but how about the second one?

• The second type used to be known as "quadratic equations" when I was at school - but that was a very long time ago! The first type looks like a simple equation - though if there really are four unknowns, you are way beyond me.
– WS2
Aug 5, 2022 at 6:48
• Have you checked the bilingual dictionary? Aug 5, 2022 at 7:48
• @WS2 a quadratic equation is one where a term is squared (multiplied by itself). The term derives from the latin quadratus (made square). The second equation is not a quadratic equation, because no term is multiplied by itstelf. Both are linear equations cuemath.com/algebra/linear-equations Aug 5, 2022 at 10:14
• @JavaLatte Apologies - it's been a long time!
– WS2
Aug 5, 2022 at 13:12
• @javalatte the second equation is also a linear equation? Aug 5, 2022 at 15:06

Looking at the expressions on the right-hand-side of the two formulae:

The first expression is a sum of three terms: a, b and -c.

Longer sums (especially when written with Σ notation) are also called series.

The second expression is product of three factors a, b and c-1

What about "linear equations". Well this is maths, not English learning. An equation is linear if it is in the form y = A x (where "A" is a constant (possibly a matrix), and x and y are (possibly vector) variables), or in some contexts if y=ax + b. However you say that a, b, c "could be a complex term, or a single known or unknown value." and so these equations are not in general linear.

If you consider x,a,b and c all to be variables, then "x = a+b+c" is linear (it could be written in matrix form x = (1 1 1)(a b c)T) The second is not linear, or non-linear.

• thank you so much! Clearly, the question is more complicated than I thought. Yes, I'll go for 'linear' and 'non-linear' with some extra explanation about the formulas. Aug 5, 2022 at 17:11

The expression on the right-hand side of the first equation (a + b - c) is a "trinomial", and the expression on the right-hand side of the second (a * b / c) is a "monomial". (You could therefore call the equations a "trinomial equation" and a "monomial equation", but those expressions aren't very common.)

The equations can also be classified according to their degree, and I think that some people have gotten confused because you don't specify what a, b, and c are.

• If all three letters are constants, then both equations are constant.
• If either a or b is a variable (and the other two letters are constants), then both equations are linear.
• If at least two of those letters are variables, then the first equation is linear but the second isn't.

These are arithmetic expressions and you could say arithmetic equations or arithmetical equations if you needed to insist that they are equations.

The first example is in Presburger_arithmetic and the second in Peano arithmetic, which are theories of the natural numbers, but both are highly technical and wouldn't be understood by a general audience

• This answer assumes that these are assignment in a computer language, but the OP mentions maths, the reference to Presburger and Peano arithmetic is confusing and incorrect. There is no suggestion or requirement that a, b, c represent natural numbers. Peano arithmetic has no "division" operation. There is no technical nor colloquial context in which you would say "a * b / c is an expression in Peano arithmetic" Aug 5, 2022 at 9:59
• In mathematics, there is a distinct difference between equation and expression and the two terms cannot be used interchangeably. An equation has an equals sign, an expression does not. Aug 5, 2022 at 12:38